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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.13451 |
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| _version_ | 1866915583787794432 |
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| author | Reboulet, Rémi Nyström, David Witt |
| author_facet | Reboulet, Rémi Nyström, David Witt |
| contents | We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded filtration F of the section ring of L, the set of bounded decreasing convex functions on the support of the Duistermaat--Heckman measure of F embeds L^p-isometrically into the space of bounded positive metrics on L with respect to Darvas' d_p distance for all p\in[1,\infty), and in particular with respect to the Mabuchi metric (p=2). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13451 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinite-dimensional flats in the space of positive metrics on an ample line bundle Reboulet, Rémi Nyström, David Witt Differential Geometry Algebraic Geometry We show that any continuous positive metric on an ample line bundle L lies at the apex of many infinite-dimensional Mabuchi-flat cones. More precisely, given any bounded graded filtration F of the section ring of L, the set of bounded decreasing convex functions on the support of the Duistermaat--Heckman measure of F embeds L^p-isometrically into the space of bounded positive metrics on L with respect to Darvas' d_p distance for all p\in[1,\infty), and in particular with respect to the Mabuchi metric (p=2). |
| title | Infinite-dimensional flats in the space of positive metrics on an ample line bundle |
| topic | Differential Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2311.13451 |